Without checking, I think ἀπραγμοσύνη here means leisure or freedom from other business that could divert the author's attention from philosophy. I don't think your translation is quite correct, though out of context it's hard to tell. ἵν᾿ ἔχω seems to mean "so that I might have" leisure, not "I offer".

It seems strange for a Christian saint to have ἐρασταί, but perhaps the word has a more Platonic meaning in this context than in Plato.